Let me speak from my own personal experience, which is as a former legal counsel to the Copyright Board of Canada, without speaking about any individual office-holder.
Parliament enacts the Copyright Act, and the Copyright Act contains provisions constituting the Copyright Board. It empowers the board to do certain things and indicates who may hold office as a Copyright Board member to carry out those functions.
Once Parliament has specified what the role of that board would be, how members are to be appointed, and on what terms, there is no longer a role for Parliament to play in supervising how the executive implements those instructions contained in the legislation.
So at that point the relationship concerns solely the Governor in Council or the executive branch of government and the office-holder him or herself.
I believe what you're asking is whether there might be a role for Parliament to play after that point, should Parliament wish to supervise what the executive branch of government is doing.